Interference fringe, a bright or dark band caused by beams of light that are in phase or out of phase with one another. Light waves and similar wave propagation, when superimposed, will add their crests if they meet in the same phase (the waves are both increasing or both decreasing); or the troughs will cancel the crests if they are out of phase; these phenomena are called constructive and destructive interference, respectively. If a beam of monochromatic light (all waves having the same wavelength) is passed through two narrow slits (an experiment first performed in 1801 by Thomas Young, an English scientist, who inferred from the phenomenon the wavelike nature of light), the two resulting light beams can be directed to a flat screen on which, instead of forming two patches of overlapping light, they will form interference fringes, a pattern of evenly spaced alternating bright and dark bands. All optical interferometers function by virtue of the interference fringes that they produce.\
Young's Double-Slit Experiment verifies that light is a wave simply because of the bright and dark fringes that appear on a screen. It is the constructive and destructive interference of light waves that cause such fringes.
Constructive Interference of Waves
The following two waves ( Fig. 1 ) that have the same wavelength and go to maximum and minimum together are called coherent waves. Coherent waves help each others effect, add constructively, and cause constructive interference. They form a bright fringe.
Destructive Interference of Waves
In Fig. 2 however, the situation is different. When wave with amplitude A1 is at its maximum, wave with amplitude A2 is at its minimum and they work against each other resulting in a wave with amplitude A2 A1. These two completely out of phase waves interfere destructively. If A2 = A1, they form a dark fringe.
The bright and dark fringes in the Youngs experiment follow the following formulas:
Bright Fringes: d sin(θk) = k λ where k = 0,1,2,3, ...
Dark Fringes: d sin(θk) = (k + 1/2) λ where k = 0,1,2,3, ...
The above formulas are based on the following figures:
Check the following statements for correctness based on the above figure.
Light rays going to D2 from S1 and S2 are 3(� λ) out of phase (same as being � λ out of phase) and therefore form a dark fringe.
Light rays going to B1 from S1 and S2 are 2(� λ) out of phase (same as being in phase) and therefore form a bright fringe.
Note that SBo is the centerline.
Going from a dark or bright fringe to its next fringe changes the distance difference by � λ.